Telomeres, complexes of DNA and proteins, protect ends of linear chromosomes. In humans, the two shelterin proteins TRF1 and TIN2, along with cohesin subunit SA1, were proposed to mediate telomere cohesion. Although the ability of the TRF1-TIN2 and TRF1-SA1 systems to compact telomeric DNA by DNA-DNA bridging has been reported, the function of the full ternary TRF1-TIN2-SA1 system has not been explored in detail. Here, we quantify the compaction of nanochannel-stretched DNA by the ternary system, as well as its constituents, and obtain estimates of the relative impact of its constituents and their interactions. We find that TRF1, TIN2, and SA1 work synergistically to cause a compaction of the DNA substrate, and that maximal compaction occurs if all three proteins are present. By altering the sequence with which DNA substrates are exposed to proteins, we establish that compaction by TRF1 and TIN2 can proceed through binding of TRF1 to DNA, followed by compaction as TIN2 recognizes the previously bound TRF1. We further establish that SA1 alone can also lead to a compaction, and that compaction in a combined system of all three proteins can be understood as an additive effect of TRF1-TIN2 and SA1-based compaction. Atomic force microscopy of intermolecular aggregation confirms that a combination of TRF1, TIN2, and SA1 together drive strong intermolecular aggregation as it would be required during chromosome cohesion.